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A helicopter just circulates air in a hover and maintains a stable altitude. So, how much energy is used to do this? Using the standard equation $KE = \frac12 mv^2$; then the kinetic energy used would be $0.5$ times the mass of air displaced down each second ($m$), times the vertical velocity of this air squared ($v^2$). Is this correct?
I couldn't find this in any engineering textbook. Estimates (guesses) from fuel burn is helpful, but are very inaccurate; as they rely on estimates (assumptions) of how efficient the fuel conversion to mechanical energy is, how efficient the motor is at using this energy, and then how efficient the rotors are at displacing air down. Which is too many assumptions.